What you are describing actually sounds normal to me, not like they are shrink-wrapped. As the baby begins to zip around the top, the membrane at the edges will naturally dry out and look white. The part that shrink-wraps is *inside* the egg and you wouldn't be able to see it--the babies would just get stuck and stop making progress. When this happens, you have up to three days before they will die in there--they have just finished storing up the energy from the yolk and won't need to eat or drink for a long time, so you are far better off giving them time and waiting than trying to help too soon.
You said that they are zipping around the egg--how long are you giving them to complete the process? In ducks it can take several hours, although in chickens I think it is a little faster. If they start to zip and then stop making progress for several hours, that is when you should interfere.
The one that you helped--did it still have yolk hanging out of its belly, or was it fully absorbed?
Also, how is your temp? Is it possible that it's too hot in there? That would cause them to get exhausted and to breathe poorly and possibly get stuck in their shells from heat exhaustion.
I don't understand what you mean by the "fuzz" came off with the top part of the egg. First of all, the small end of the egg is the bottom... you don't have them upside down, do you? And do you mean the fuzz on the chick's head? Did it come off the chick's head?
Sorry if I'm not helping much, but so far I'm not sure I understand the problem very clearly. It sounds pretty much like normal, unless they are starting to zip and then not making progress for several hours at a time. But if they are just taking a long time--that's totally normal.
If you helped the one out too soon, it will be weak at first because it won't have had a chance to absorb its yolk sac, and may have lost blood during the process (did the membrane bleed while you were helping?). But unless there's something wrong with it other than the early hatch, it should be fine. On the other hand, it's also possible there's something else going on here--disease, or congenital problems, etc. But I suspect it's just a slow but normal process...